
where \(\phi _u = -\nabla {\operatorname{u}}^\top {\operatorname{\theta }}\) , \(\phi _v = -\nabla {\operatorname{v}}^\top {\operatorname{\theta }}\) , \(\phi _p = -\nabla p\cdot {\operatorname{\theta }}\) , and \(\phi _\pi = -\nabla \pi \cdot {\operatorname{\theta }}\) , which were generated by using the identity \(\frac{d}{dt}(\varphi \circ T_t^{-1}) = -\nabla \varphi \cdot {\operatorname{\theta }},\)  for \(\phi \in H^1(D)\)  [1]}.
